Econ 145: Practice Questions II Ichiro Obara March 11, 2010 1. Consider the second price auction with three bidders . (a) If ( v 1 ,v 2 ,v 3 )=(0 . 5 ,0 . 7 ,0 , 2) , who wins and pays how much? (b) Compute the expected revenue for the seller in dominant strat-egy equilibrium when the distribution of each bidder’s value is uniform on [0 , 1] . (c) Suppose that a reserve price is set to 0 . 2, that is, each bidder needs to bid more than 0 . 2 to win. If no one’s bid is higher than0 . 2 , then the object will not be sold. Otherwise the highest bidder wins and pays the higher value between the second highest bid and 0 . 2 . Compute the expected payment of a bidder when his or her value is 0 . 5 . (d) Compute the seller’s expected revenue when the reserve price is0 . 2 . (e) Do the same exercise as (d) when the seller’s reserve price is 0 . 5 . 2. Suppose that 3 bidders are competing for 2 links in a Pay-per-Click auction. The top link generates 100 clicks every day, and the second

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